Hello sinaumedia friends. Did you know? part of the math exercises for grades 5 to 6 of elementary school semester 2 is discussing material about building spatial shapes. The beam has several elements, including edges/planes, ribs, vertices, diagonal planes, spatial diagonals, and diagonal planes.
So, in this article, sinaumedia will share complete information, from understanding, formulas, futures, sample questions to templates for beam nets. We encounter many block-shaped objects around us, such as cupboards, pencil cases, refrigerators and others. Before going any further, it’s a good idea to know in advance what is meant by a net of blocks? and what are its characteristics
Definition of Beam Nets
The definition of beam mesh is that the beam sides are stretched relative to the tendons and, when combined, can create voids. Other terms also exist, namely several flat shapes from the division of buildings or beams.
Between blocks and cubes, both have nets that can be obtained by opening or dissecting the shape of the room until all surfaces are visible. Take a look at the next block grid image, which stays blocky at first until it opens and you can see the edges
If a beam is stretched, then the beam will form a beam lattice. There are many types of models, the following are examples of beam nets:
The combination of these edges can be called a grid of beams only if the shape of the sides of the mesh is bent to form the shape of a space. Build a block room that has a wide variety of grids. However, before making beam nets, it is important to understand the characteristics of beams first
Beam Features
1. Ribs
The rib of the beam is the line of intersection between the sides of the beam. The characteristics of the beam have a total of 12 ribs of the same length. These ribs are divided into 4 base ribs, 4 upright ribs, and 4 upper ribs. Parallel ribs have the same length
4 long ribs = AB = DC = EF = HG
4 wide ribs = AD = BC = EH = FG
4 high ribs = AE = BF = CG = DH
2. Diagonal Space
The characteristics of the beam is the diagonal space. Each space diagonal on the beam has the same length. The space diagonal of a cuboid is a line segment that connects two opposite corners of the cuboid. The space diagonals of the cuboids intersect in the middle and bisect the space diagonals equally. There are 4 space diagonals on a cuboid with the same length
3. Has 6 Sides
The side of a beam becomes the boundary between the beam and three pairs of sides that have the same shape and size when facing each other. A block must have 6 square or rectangular sides. These sides are on the left and right, up and down, and front and back
Based on the example of the beam image above, the 6 sides are: Left side and right side = ADHE = BCGF
Base (bottom) and top = ABCD = EFGH
Front side and back side = ABFE = DCGH
4. Diagonal Side
The diagonal side / plane of a beam is a line segment that connects two opposite corner points on a side. There are 12 side diagonals on the beam. Each plane diagonal on opposite sides is the same length
5. Diagonal Field
The diagonal of a beam is a plane that passes through two opposite edges. The diagonal of the beam divides the beam into two equal parts. There are 6 diagonal fields. Each diagonal plane on the beam has a rectangular shape
If you pay attention to the example of a beam image, the 6 diagonal fields are:
ACGE = BDHF diagonal plane
ABGH = DCFE diagonal plane
Diagonal plane BCHE = ADGF
6. Beam Nets
The net of beams is a flat shape which is a certain series of two squares and six congruent rectangles in such a way that when folded on the common edges it can form a beam.
7. It has a surface area and a volume of a block
A block has a surface area and a volume. Volume refers to the width of a room in a building. To determine the area and volume of a beam can be found by using certain formulas.
The Difference between Nets of Blocks and Cubes
Nets on blocks are actually not that different from nets on cubes, the difference itself is only in the shape of the sides of the blocks and cubes. Meanwhile, the method of cutting itself is the same between the two, if you start from a different side it will produce a different shape as well
The nets on cubes have side shapes only in the form of squares while the sides on the nets of blocks consist of squares and rectangles. and Nets of Blocks and Cubes
How to make beam nets
Since a cuboid is a three-dimensional figure formed by three pairs of squares or rectangles, at least one pair of them has a different size. A block has 6 sides, 12 edges and 8 vertices. A block formed by six congruent squares is called a cube. So the way to make nets of blocks is in the following way
Here is the procedure for making beam nets
- Print a pattern on the cardboard
- then, cut the cardboard following the visible line segments
- Make folds on each web based on line segments to form almost perfect beams
- The beam is the result of folding and gluing the mesh tongues, and with the lower rectangle as the front side
Examples of Formulas and Problems Calculating the Areas of Beam Nets
The formula for the surface area of a block
From the image above, we know that the block has 3 pairs of rectangles that are the same size. To calculate the surface area, we simply add up the areas of the three pairs of rectangles. There are 2 ways, namely:
Method 1: Calculate the area of three pairs of sides
L = pl + lt + pt + pl + lt + pt
L = 2pl + 2lt + 2pt
L = 2 (pl + lt + pt)
Method 2: Using the prism surface area principle
That is calculating the area of the base, roof and covers. Because the base area = roof area, the formula is obtained
L = 2 × Base area + Blanket Area
L = 2 × Base area + Base circumference × height
L = 2 × pl + (p + l + p + l) × t
L = 2pl + (2p + 2l) × t
L = 2pl + 2lt + 2pt
L = 2 (pl + lt + pt)
The result is the same. So it can be concluded that the formula for the surface area of a beam is L = 2 (pl + lt + pt) .
The surface area of a beam is the sum of the areas of all sides of a beam. There are six sides to the cuboid, with three pairs of sides that are a pair of equal sizes. Thus the surface area of the beam is equal to the sum of the three sides on the beam multiplied by two. The formula for finding the surface area of a beam can be determined in the following way: L base = L roof = p × l L front side = L back side = p × t L right side = L left side = l × t Thus, the formula for surface area of a beam is L = 2 × (pl + pt + lt). Example problem: The length, width, and height of a closed block are 8 cm, 6 cm, and 4 cm, respectively. Calculate the surface area of the block
Examples of Surface Area Problems of Beam Nets
1. A block has a length of 20 cm, a width of 14 cm and a height of 10 cm. determine the surface area of the block? The solution:
is known :
p = 20
l = 14
t = 10
So L. Surface of the Block =2(p+pt+lt)
= 2 x (20×14) + (20×10) + (14 x 10)
= 2 x (280 + 200 + 140)
= 2 x 620
= 1240 cm2
So, the surface area of the block is 1240 cm2
2. If a block has a volume of 480cm3 with a length and width of the sides respectively 10cm and 8cm. Then determine the height of the block? And calculate the total surface area? The solution: Sketch:
Its volume = 480 cm3
P=10
L = 8
In order to find out the height of the block, we use the formula for the volume of the block:
V. beam = pxlxt
480 cm³= 10 x 8 x h
480 cm³= 80 t
t = 480 : 80
t = 6 cm
The height of the beam that we have is 6 cm
Then we look for the surface area by using the formula for calculating the surface area
L.beam surface=2(pl+pt+lt)
= 2(10×8+10×6+8×6)
= 2 (80 + 60 + 48)
= 2 x 188
= 376 cm²
So, the surface area of the block is 376 cm2
3. A block has a volume of 580cm3 then the length and width on its sides are 40cm and 10cm. So what is the height of the block? And what is the total surface area? Answer:
Is known:
Volume = 580 cm3
P=40
L = 10 To find the height of the block above, we use the formula for the volume of the block: V . beam = pxlxt
580 cm³= 40 x 10 x h
580 cm³= 400 t
t = 480 : 400
t = 1.2 cm
Then the height of the block is 1.2 cm. After knowing the height, we can only find the surface area:
L.surface=2(pl+pt+lt)
= 2 (40 x 10 + 40 x 1.2 + 10 x 1.2)
= 2 (400 + 48 + 12)
= 2 x 460
= 920 cm²
So the surface area of the block is 920 cm2
4. Calculate the surface area of a cuboid that has a length of 9 cm, a width of 8 cm and a height of 7 cm
Is known
p = 9 cm
l = 8 cm
t = 7 cm
asked
L = ?
L = 2 (pl + lt + pt)
L = 2 (9×8 + 8×7 + 9×7)
L = 2 (72 + 56 + 63)
L = 2 × 191
L = 382 cm²
So, the surface area of the block is 382 cm²
5. Example questions: Length (PQ) = 6cm, Width (PS) = 4cm, Height (PT) = 3cm, what is the surface area? then the way to calculate it is as follows:
Answer
L = 2 (PQ.PS + PQ.PT + PS.PT)
= 2 (6.4 + 6.3 + 4.3)
= (2X6X4) + (2X6X3) + (2X4X3)
= 48 + 36 + 24
= 108 cm²
6. The length, width, and height of a closed block are 8 cm, 6 cm, and 4 cm, respectively. Calculate the surface area of the block. Answer:
Given: p = 8 cm; l = 6 cm; t = 4 cm
L = 2 × (pl + pt + lt) L = 2 × (8×6 + 8×4 + 6×4)
L = 2 × (48 + 32 + 24) L = 2 × 104 L
= 208 cm2
7. To find the surface area of a block, you can use the formula to calculate the surface area, as below:
Block surface area
= 2 (pl + pt + lt)
= 2 (10 x 8 + 10 x 6 + 8 x 6)
= 2 (80 + 60 + 48)
= 2 x 188
= 376 cm²
So that it can be determined if the surface area of the block is 376 cm2
Examples of Formulas and Problems Calculating the Volume of Beam Nets
Block Volume Formula
The volume of the beam is the size of the space that is bounded by the sides of the beam. To calculate the volume of a block (V), it is necessary to know the length, height and width of the block. The formula for the volume of a cuboid is V = p × l × t. The unit for the volume of a block is cubic written with cubes, for example cubic centimeter (cm3) and cubic meter (m3).
Example of a Block Volume Problem
1. A cuboid has a length of 7 cm, a width of 4 cm and a height of 3 cm. Then the volume of the block is?
Is known:
p = 7 cm; l = 4 cm; t = 3 cm
V = p × w × t
V = 7 × 4 × 3
V = 84 cm3 J
So, the volume of the block is 84 cm3
2. Calculate the height of the block if it is known:
V = 24 cm³
p = 4 cm
l = 3 cm
Answer: V = pxlxt
24 = 4 x 3 x t
24 = 12 xt
t = 24 : 12
t = 2 cm
3. The volume of wooden blocks purchased by Mr. Kasno is
V = pxlxt
V = (8) x (1) x (1)
V = 8 m3
Since every 1 m3 of wood costs Rp. 10,000, the price of the wooden blocks Mr. Budi buys is
Price = 8 x 10,000 = IDR 80.00
The initial volume of pool water = 600 L
Remaining final water volume = 1/3 x 600 = 200 L. This value is converted in m3 to 0.2 m3
It is known that the area of the pond base = 2 m2
4. The height of the remaining water in the pool can be calculated using the basic formula for the volume of a block
V = pxlxt
V = (pxl)xt
V = (Base area) xt
0.2 = 2 xt
t = 0.1 m
t = 10 cm
With that, the pool water level after draining is 10 cm
5. A rectangular bathtub is 100 cm long, 60 cm wide and 80 cm high. How many liters of water are needed to fill 2/3 of the tub?
Answer:
Bathtub volume = pxlxt
Bathtub volume = 100 x 60 x 80
Bath volume = 480,000 cm³ = 480 dm³ = 480 liters
Volume of 2/3 bath = 2/3 x 480
Volume 2/3 bath = 320 liters
So, the water needed to fill 2/3 of the bath is 320 liters
6. A box of rice is in the shape of a block with a length of 30 cm, a width of 25 cm and a height of 0.5 m. The rice box is planned to be filled with rice for Rp. 10,000/liter. How much money is used to buy rice until the rice box is full?
Answer:
the length of the block = 30 cm
beam width = 25 cm
block height = 0.5 m = 50 cm
Rice box volume = pxlxt
Rice box volume = 30 x 25 x 50
Rice box volume = 37,500 cm³ = 37.5 liters
Price of rice = 37.5 x IDR 10,000
Price of rice = IDR 375,000
So, the amount of money used to buy rice is IDR 375,000
7. If an ice cube in the form of a block has the following internal dimensions: length 50 cm, width 40 cm, and height 40 cm. Then the block-shaped ice cubes are filled with water to a height of 30 cm. Calculate the volume of water in the block of ice?
Discussion
Look at the story carefully. Here what you are told to look for is the volume of water filled in the block-shaped ice, not the volume of the block itself
Water Volume = length x width x height of water
Water Volume = 50 x 40 x 30
Water Volume = 60,000 cm3
8. If an aquarium has the following inner dimensions: 50 cm long, 40 cm wide and 40 cm high. Then the aquarium is filled with water to a height of 30 cm. Calculate the volume of water in the aquarium?
Discussion
Look at the story carefully. Here what you are told to look for is the volume of water filled in the Aquarium, not the volume of the Aquarium itself
Water Volume = length x width x height of water
Water Volume = 50 x 40 x 30
Water Volume = 60,000 cm3